Английская Википедия:Euler's differential equation

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In mathematics, Euler's differential equation is a first-order non-linear ordinary differential equation, named after Leonhard Euler. It is given by:[1]

<math>\frac{dy}{dx} + \frac{\sqrt{a_0+a_1y +a_2 y^2 + a_3 y^3 + a_4 y^4}}{\sqrt{a_0+a_1x +a_2 x^2 + a_3 x^3 + a_4 x^4}} = 0</math>

This is a separable equation and the solution is given by the following integral equation:

<math>\int \frac{dy}{\sqrt{a_0+a_1 y + a_2 y^2 + a_3 y^3 + a_4 y^4}} + \int \frac{dx}{\sqrt{a_0+a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4}} = c </math>

References

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Шаблон:Math-physics-stub

  1. Ince, E. L. "L. 1944 Ordinary Differential Equations." 227.